Do your starter wire connections look like this:
Provided you're certain you've got all the wires hooked up to the right location, ticky but no-startie usually means a bad solenoid internal connection (copper contacts that close to send full amps to the starter). Sounds like your starter is fine, but no juice is being connected to it via the solenoid when it closes.
The part that's funny and probably a tell-tale sign is that the car stumbles and runs poorly after started and the remote jumper battery is removed. Alternator diode bad, perhaps?
Sorry not much help. Hang in there, lots of people out there with intimate starter knowledge.